document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185600>Question 1185600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the exact values of the other five trigonometric<BR>\n" );
document.write( "functions of θ.<BR>\n" );
document.write( "csc θ = −2 and cot θ > 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816427 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cotangent is equal to 1/tangent, which is  positive in quadrant 1 and quadrant 3, and negative in quadrant 2 and 4.<BR>\n" );
document.write( "cosecant is equal to 1/sine, which is positive in quadrant 1 and 2, and negative in quadrant 3 and 4.<BR>\n" );
document.write( "if the cosecant, which is equal to 1/sine, is negative and the cotangent, which is equal to 1/tangent, is positive, you have to be in quadrant 3.\r<BR>\n" );
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document.write( "you are given that cosecant theta = -2.<BR>\n" );
document.write( "this means that 1/sine theta = -2.<BR>\n" );
document.write( "solve for sine theta to get:<BR>\n" );
document.write( "sine theta = -1/2.\r<BR>\n" );
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document.write( "in the first quadrant, sine theta would be equal to 1/2 and the angle would be equal to 30 degrees.<BR>\n" );
document.write( "the same angle in the third quadrant is equal to 180 + 30 degrees = 210 degrees.\r<BR>\n" );
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document.write( "the sine of 210 degrees is equal to -1/2.<BR>\n" );
document.write( "the cosecant of 210 degrees is equal to 1/sine 210 degrees = 1/(-1/2) = -2.\r<BR>\n" );
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document.write( "the cosine of 210 degrees is equal to -sqrt(3)/2.<BR>\n" );
document.write( "the secant of 210 degrees is equal to 1/cosine 210 degrees = 1/(-sqrt(3)/2) = 2/-sqrt(3) = -2*sqrt(3)/3.\r<BR>\n" );
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document.write( "the tangent of 210 degrees is equal to -1/-sqrt(3) = 1/sqrt(3) = sqrt(3)/3.<BR>\n" );
document.write( "the cotangent of 210 degrees is equal to 1/(sqrt(3)/3) = 3/sqrt(3) = 3*sqrt(3)/3 = sqrt(3).\r<BR>\n" );
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document.write( "the following diagram shows you what the angle looks like in quadrant 3 where it resides.\r<BR>\n" );
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document.write( "the reference angle is the equivalent angle in the first quadrant.<BR>\n" );
document.write( "it has the same trigonometric function values except for the sign.<BR>\n" );
document.write( "in the first quadrant all the trigonometric values are positive.<BR>\n" );
document.write( "in the third quadrant, the trigonometric functions have the same values, excpt:<BR>\n" );
document.write( "sine and cosecant are negative.<BR>\n" );
document.write( "cosine and secant are negative.<BR>\n" );
document.write( "tangent and cotangent are positive.\r<BR>\n" );
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document.write( "here are the trigonometric values of the special angles, 30 degrees and 210 degrees being among them.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mcckc.edu/tutoring/docs/br/math/calc_trig/Special_Angles_Chart.pdf\" target = \"_blank\">https://www.mcckc.edu/tutoring/docs/br/math/calc_trig/Special_Angles_Chart.pdf</a>\r<BR>\n" );
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document.write( "30 degrees and 210 degrees are highlighted below.\r<BR>\n" );
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